MST 3102 university of Guyana Regression Analysis Practice Quiz

University of GuyanaFaculty of Natural Sciences
Semester I 0f 2021-22
MST 3102 (Regression Analysis)
Date and Time: Friday 11th March, 2022 10:00.
Duration: 1 hr.
Instructions to Candidates:
Answer ALL questions
1. From some statistical analysis, we have the following table
X in model
None
X1
X2
X3
X4
X1 , X2
X1 , X3
X1 , X4
X2 , X3
X2 , X4
X3 , X4
X1 , X2 , X3
X1 , X2 , X4
X1 , X3 , X4
X2 , X3 , X4
X1 , X2 , X3 , X4
R2
C
0.000 1721.6
0.120 1510.8
0.352 1100.1
0.442 939.0
0.527 788.2
0.438 948.7
0.646 580.2
0.528 789.4
0.813 283.7
0.650 573.5
0.687 507.9
0.972
3.0
0.650 574.8
0.719 452.0
0.883 161.7
0.972
5.0
(a) Assume that it is possible to use the C statistic for model building. Use the C statistic,
to determine the best model using forward selection. Justify your selection at
each step.
[8 marks]
(b) Determine the best model overall based on the C statistic. Justify your answer.
[2 marks]
(c) Determine the best model overall based on R2 . Justify your answer.
[2 marks]
2. A regression model is estimated for the dependent variable, y, on x1 and x2 . The following
are all results from this estimation.
Chart A
Chart B
Chart C
Chart D
(a) By testing a suitable hypothesis, determine whether the model is a useful representation of the relationship between the dependent and the independent variables.
Provide evidence for your conclusion.
[3 marks]
(b) How useful would you say that the model is for predicting y?
[2 marks]
(c) Determine which, if any, of the assumptions of a Least Squares Regression are
violated. Justify your answer.
[6 marks]
(d) Do the data appear to be affected by outliers? Justify your answer.
End of Test
Page 2
[3 marks]
X2
1. From some statistical analysis, we have the following table
X in model R” с
None
0.000 1721.6
X
0.120 1510.8
0.352 1100.1
X3
0.442 939.0
X4
0.527 788.2
X1, X2
0.438 948.7
X1, X3
0.646 580.2
X1, X4
0.528 789.4
X₂,
X₃ 0.813 283.7
X₂, X, 0.650 573.5
X3, X,
0.687
507.9
X1, X2, X3 0.972 3.0
X1, X2, X4 0.650 574.8
X1, X3, X4 0.719 452.0
X2, X3, X4 0.883 161.7
X1, X2, X3, X4 0.972 5.0
(a) Assume that it is possible to use the statistic for model building. Use the statistic,
to determine the best model using forward selection. Justify your selection at
each step.
[8 marks)
(b) Determine the best model overall based on the statistic. Justify your answer.
[2 marks]
(c) Determine the best model overall based on R². Justify your answer. [2 marks]
2. A regression model is estimated for the dependent variable, y, on 1 and 19. The following
are all results from this estimation.
. reg y x1 x2
Source
SS
df NS
Number of obs = 15
FC 2 12) = 563.43
Mode! 171754.701 2 85877.3506
Prob F
0.0000
Residual 1829.03208 12 152.41934
R-squared = 0.9895
Adj R-squared = 0.9877
Total 1 173583.733 14 12398.8381
Root MSE
12.346
у |
t
P>It
x
Coef.
6.327888
3.723111
-199.7852
Std. Err.
2037353
1.513925
11.53184
31.06
2.46
-17.32
0.000
0.030
0.000
(95% Conf. Interval]
5.883987 6.771789
4245518 7.02167
-224.911 -174.6595
_cons
1.
1.
HO
Chart A
Chart B
1-
1
Chart C
Chart D
(a) By testing a suitable hypothesis, determine whether the model is a useful repre-
sentation of the relationship between the dependent and the independent variables.
Provide evidence for your conclusion.
[3 marks)
(b) How useful would you say that the model is for predicting y? [2 marks]
(c) Determine which, if any, of the assumptions of a Least Squares Regression are
violated. Justify your answer.
[6 marks)
(d) Do the data appear to be affected by outliers? Justify your answer. [3 marks)
a